Perhaps the informal translation of the word is different in your dialect? Here it means crazy as in loopy or delusional. I do not believe it to have any connotation to rage, anger or frustration.

-I just decided to look it up to see. The first definition given was the informal adjective for "mad." So I assume this is what you were thinking.

The third defintion is;

informal
a crazy or eccentric person.
"she would have written me off as a time-wasting nut"
synonyms: madman/madwoman, maniac, lunatic

I meant more along these lines.

But I would replace the example sentence with;

He really thought he could save the world- all on his own? He must have been nuts.

If you read it again now, I think the word should make absolute sense within the context.